Background

This document has nls (non-linear least squares) regression fits using the LOG-NORMAL functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) Biomass growth vs. stand biomass relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Log-Normal functional form \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge /c \right)} {d} \right]} ^2 \right)\), where \(B\) is the plot biomass, \(StdAge\) is the stand age at time of biomass measurement, \(\Delta PDSI\) is the difference in the 9-month annual average PDSI (excluding the winter months, i.e., January-September) over the FIA plot biomass interval, which is defined as the measurement time minus 10 years and a 30-year climate normal from 1960 to 1989, and \(yr\) is the measurement year. Free parameters are: \(ge\): biomass growth enhancement over time, \(\phi\): the effect of climate dryness on stand biomass, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(B\), \(c\): the \(StdAge\) value at peak \(B\), and \(d\): the log-normal curve shape parameter.

Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using the base model (i.e., excluding phi), and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).

model 1: simple model \(B = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(B_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 2: phi model \(B = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(B_{t1} /c \right)} {d} \right]} ^2 \right)\)

Note:

This analysis uses ALL available plot biomass data

which includes the following plot-based filtering criteria:

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9936     2501.4                                
## 2   9935     2488.4  1 13.012   51.95 6.107e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 107696.3
## 2     2 107646.5
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.241234   0.106391  -2.267   0.0234 *  
## phi   0.048121   0.006438   7.474 8.41e-14 ***
## a    28.841474   1.209812  23.840  < 2e-16 ***
## b   131.423715   4.344807  30.248  < 2e-16 ***
## c   126.036776   5.371817  23.463  < 2e-16 ***
## d     1.102377   0.040252  27.387  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5005 on 9935 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1  30368      10474                          
## 2  30359      10474  9 0.31831  0.1025 0.9996
##   model      AIC
## 1     1 316275.7
## 2     2 316195.9
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.11401    0.06468   1.763    0.078 .  
## phi   0.00000    0.00308   0.000    1.000    
## a    14.45284    0.39879  36.242   <2e-16 ***
## b    92.71935    1.75123  52.945   <2e-16 ***
## c   128.41078    4.06060  31.624   <2e-16 ***
## d     1.45470    0.02883  50.462   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5874 on 30359 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (30 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1  11287     2103.2                           
## 2  11286     2103.2  1 0.009898  0.0531 0.8177
##   model      AIC
## 1     1 123636.4
## 2     2 123638.3
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.01701    0.07494   0.227     0.82    
## a   21.66715    1.50287  14.417   <2e-16 ***
## b  174.62875    6.69913  26.067   <2e-16 ***
## c  154.79638   10.92491  14.169   <2e-16 ***
## d    1.50194    0.05919  25.375   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4317 on 11287 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   7907     2576.2                         
## 2   7906     2576.1  1 0.0527  0.1617 0.6876
##   model      AIC
## 1     1 85260.52
## 2     2 85262.36
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.18074    0.11196  -1.614    0.106    
## a   16.59776    1.14643  14.478   <2e-16 ***
## b  126.23170    4.51869  27.935   <2e-16 ***
## c  116.00466    5.95712  19.473   <2e-16 ***
## d    1.22690    0.04757  25.791   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5708 on 7907 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1  13434     2573.5                              
## 2  13433     2573.5  1 -3.4379e-10       0      1
##   model      AIC
## 1     1 140618.9
## 2     2 140620.9
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.01578    0.06557  -0.241     0.81    
## a   21.63233    1.44962  14.923   <2e-16 ***
## b  109.74919    2.96451  37.021   <2e-16 ***
## c  116.08499    5.44770  21.309   <2e-16 ***
## d    1.44349    0.05263  27.427   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4377 on 13434 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1  19930     6319.4                              
## 2  19929     6319.4  1 -9.2132e-10       0      1
##   model    AIC
## 1     1 217248
## 2     2 217250
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.68806    0.07597   9.057   <2e-16 ***
## a   13.36056    0.44646  29.925   <2e-16 ***
## b  144.78186    4.29070  33.743   <2e-16 ***
## c  142.55533    9.68371  14.721   <2e-16 ***
## d    1.87326    0.04721  39.677   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5631 on 19930 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (26 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  20856     9549.0                                
## 2  20853     9539.3  3 9.7429  7.0994 9.174e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 232202.4
## 2     2 232164.9
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  2.320e-01  7.386e-02   3.141  0.00169 ** 
## phi 1.491e-02  5.111e-03   2.917  0.00354 ** 
## a   1.315e+01  5.339e-01  24.639  < 2e-16 ***
## b   1.650e+02  6.700e+00  24.629  < 2e-16 ***
## c   1.800e+02  1.714e+01  10.502  < 2e-16 ***
## d   1.970e+00  6.150e-02  32.036  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6764 on 20853 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (60 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1   2184     814.28                           
## 2   2183     812.63  1 1.6406  4.4072 0.0359 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24930.06
## 2     2 24927.64
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.12750    0.23214  -0.549 0.582893    
## phi   0.03866    0.01855   2.085 0.037219 *  
## a    18.50507    3.93531   4.702 2.73e-06 ***
## b   249.58616   75.54526   3.304 0.000969 ***
## c   306.23891  190.54750   1.607 0.108166    
## d     1.97732    0.35814   5.521 3.77e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6101 on 2183 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89486, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.753, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    240     60.621                              
## 2    239     60.621  1 -3.2081e-11       0      1
##   model      AIC
## 1     1 3071.216
## 2     2 3073.216
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.5603     0.4889  -1.146   0.2529    
## a   31.0320    23.7278   1.308   0.1922    
## b  615.5216   155.0120   3.971 9.47e-05 ***
## c  352.7609   165.3432   2.134   0.0339 *  
## d    1.8421     0.3603   5.113 6.50e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5026 on 240 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96457, p-value = 9.228e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.5226, p-value = 0.0004273
## alternative hypothesis: two.sided

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   2779     735.04                           
## 2   2778     734.99  1 0.053246  0.2013 0.6537
##   model      AIC
## 1     1 29307.39
## 2     2 29309.19
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.33624    0.15541  -2.164   0.0306 *  
## a   27.65434    2.41852  11.434   <2e-16 ***
## b  103.81353    5.49961  18.877   <2e-16 ***
## c  101.68632    6.64390  15.305   <2e-16 ***
## d    1.11177    0.07391  15.042   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5143 on 2779 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96148, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -24.414, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1   1280     483.88                            
## 2   1279     483.88  1 0.0040563  0.0107 0.9175
##   model      AIC
## 1     1 13076.50
## 2     2 13078.49
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.5129     0.2501  -2.050   0.0405 *  
## a   14.2442     2.0561   6.928 6.75e-12 ***
## b   83.0909     5.9733  13.910  < 2e-16 ***
## c   69.9975     6.5513  10.685  < 2e-16 ***
## d    1.2098     0.1009  11.991  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6148 on 1280 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94546, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.563, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

## Error in nls(f_ln_1, data = P_261, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = P_261, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: false convergence (8)
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_261.", Mod.Sel1, sep = "")) : 
##   object 'nls_261.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • unable to fit model (only 64 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_262.", Mod.Sel1, sep = "")) : 
##   object 'nls_262.' not found

summary

  • simple model: does not fit

  • phi model: does not fit

  • unable to fit model (0 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    424     97.216                              
## 2    423     97.216  1 -1.4211e-14       0      1
##   model      AIC
## 1     1 5410.454
## 2     2 5412.454
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)  
## ge 2.049e+00  8.421e-01   2.434   0.0154 *
## a  0.000e+00  5.605e+01   0.000   1.0000  
## b  1.000e+03  1.104e+03   0.906   0.3656  
## c  5.000e+03  1.852e+04   0.270   0.7873  
## d  3.487e+00  2.003e+00   1.741   0.0825 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4788 on 424 degrees of freedom
## 
## Algorithm "port", convergence message: both X-convergence and relative convergence (5)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96675, p-value = 2.737e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.1995, p-value = 5.664e-10
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    501     172.40                           
## 2    500     172.39  1 0.014962  0.0434 0.8351
##   model      AIC
## 1     1 5435.558
## 2     2 5437.514
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.78642    0.35499  -2.215   0.0272 *  
## a   25.47377    4.39240   5.800 1.18e-08 ***
## b  110.39796   11.78116   9.371  < 2e-16 ***
## c  131.74298    4.59337  28.681  < 2e-16 ***
## d    0.66796    0.05752  11.613  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5866 on 501 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9006, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.7647, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

  • model not fitted (not enough data)

summary

  • simple model: does not fit
  • phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## Warning: Removed 1 rows containing missing values (geom_segment).

plotting 2

## Warning: Removed 1 rows containing missing values (geom_segment).

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    747     494.66                              
## 2    746     494.66  1 -2.7391e-09       0      1
##   model      AIC
## 1     1 7635.544
## 2     2 7637.544
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3460     0.5299  -0.653 0.513998    
## a   10.0252     2.5769   3.890 0.000109 ***
## b   54.4545     8.0086   6.799 2.15e-11 ***
## c  129.9000    27.9390   4.649 3.94e-06 ***
## d    1.4323     0.2387   6.000 3.08e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8138 on 747 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86835, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.04, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    317     222.58                          
## 2    316     222.33  1 0.25864  0.3676 0.5447
##   model      AIC
## 1     1 3495.858
## 2     2 3497.484
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)
## ge    -0.2643     0.8434  -0.313    0.754
## a     24.2164    15.4301   1.569    0.118
## b    321.7358  2059.4978   0.156    0.876
## c   1383.2317 15422.6995   0.090    0.929
## d      2.3261     4.3085   0.540    0.590
## 
## Residual standard error: 0.8379 on 317 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.85367, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.0512, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1    141     43.589                             
## 2    140     43.589  1 7.3186e-13       0      1
##   model      AIC
## 1     1 1561.523
## 2     2 1563.523
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   1.2044     1.3718   0.878 0.381453    
## a   29.3517     8.7951   3.337 0.001082 ** 
## b   67.9425    18.5935   3.654 0.000363 ***
## c  141.8680    14.2903   9.928  < 2e-16 ***
## d    0.6582     0.1398   4.709 5.88e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.556 on 141 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96506, p-value = 0.0008963
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.3833, p-value = 0.0007162
## alternative hypothesis: two.sided

predict and plot

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(f_ln_2, data = P_342, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
##   model      AIC
## 1     1 3420.252
## 2     2       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   0.3774     1.2278   0.307 0.758792    
## a   16.8483     5.3718   3.136 0.001872 ** 
## b   48.3460    13.2043   3.661 0.000294 ***
## c  120.4151    12.1849   9.882  < 2e-16 ***
## d    0.8567     0.1812   4.729 3.42e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9198 on 314 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: does not fit`

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88507, p-value = 9.49e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.8708, p-value = 1.112e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).

411 - Everglades

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1    164     71.662                             
## 2    163     71.662  1 1.5513e-10       0      1
##   model      AIC
## 1     1 1791.752
## 2     2 1793.752
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)  
## ge    -1.3900     0.5698  -2.439   0.0158 *
## a     11.0691    25.2901   0.438   0.6622  
## b    934.1442  6742.0081   0.139   0.8900  
## c   5000.0000 75754.5925   0.066   0.9475  
## d      3.0309     5.3754   0.564   0.5736  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.661 on 164 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96756, p-value = 0.0005489
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.3815, p-value = 7.387e-08
## alternative hypothesis: two.sided

predict and plot

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  10055     1976.7                                
## 2  10054     1970.4  1 6.2748  32.018 1.569e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 106916.2
## 2     2 106886.2
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.05650    0.09138   0.618    0.536    
## phi   0.02967    0.00544   5.455 5.01e-08 ***
## a    15.08533    1.52106   9.918  < 2e-16 ***
## b   154.85207    6.93604  22.326  < 2e-16 ***
## c   186.83134   15.64827  11.939  < 2e-16 ***
## d     1.58443    0.06894  22.982  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4427 on 10054 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1  13158     2159.7                         
## 2  13157     2159.7  1      0       0      1
##   model      AIC
## 1     1 145111.3
## 2     2 145113.3
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.66998    0.07326   9.145   <2e-16 ***
## a   27.60308    1.42684  19.346   <2e-16 ***
## b  127.24722    2.60234  48.897   <2e-16 ***
## c  107.28587    3.05414  35.128   <2e-16 ***
## d    1.35134    0.03717  36.352   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4051 on 13158 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Error in nls(f_ln_1, data = P_M223, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = P_M223, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_M223$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_M223.", Mod.Sel1, sep = "")) : 
##   object 'nls_M223.' not found

summary

  • simple model: does not fit
  • phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   1482     342.11                             
## 2   1481     341.16  1 0.94375  4.0968 0.04314 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15289.65
## 2     2 15287.55
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  1.658e-01  2.521e-01   0.658   0.5108    
## phi 3.674e-02  1.853e-02   1.983   0.0475 *  
## a   3.215e+00  4.266e+00   0.754   0.4512    
## b   2.277e+02  1.231e+02   1.850   0.0646 .  
## c   8.349e+02  1.151e+03   0.725   0.4684    
## d   2.737e+00  7.004e-01   3.908 9.72e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.48 on 1481 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96879, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.544, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1   7932       4824                              
## 2   7931       4824  1 -1.0768e-09       0      1
##   model      AIC
## 1     1 105695.1
## 2     2 105697.1
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge 8.961e-03  1.632e-01   0.055    0.956    
## a  0.000e+00  7.564e+00   0.000    1.000    
## b  5.220e+02  4.142e+01  12.603  < 2e-16 ***
## c  8.633e+02  1.940e+02   4.449 8.74e-06 ***
## d  2.514e+00  1.750e-01  14.370  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7799 on 7932 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits ## plot residuals

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Warning in log(STDAGE/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_M261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_M261.", Mod.Sel1, sep = "")) : 
##   object 'nls_M261.' not found

summary

  • simple model: does not fit
  • phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot data with prediction"

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    907     273.82                          
## 2    906     273.21  1 0.60241  1.9976 0.1579
##   model      AIC
## 1     1 9513.399
## 2     2 9513.390
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.82619    0.28070  -2.943  0.00333 ** 
## phi   0.02915    0.01893   1.540  0.12387    
## a    25.27188    5.34178   4.731 2.59e-06 ***
## b   111.54653   10.25159  10.881  < 2e-16 ***
## c   150.89398   11.70684  12.889  < 2e-16 ***
## d     0.84635    0.09253   9.147  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5491 on 906 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94701, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.9897, p-value = 1.353e-15
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   5204     1792.8                           
## 2   5203     1792.8  1 0.000435  0.0013 0.9717
##   model     AIC
## 1     1 54507.6
## 2     2 54509.6
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.98350    0.09788  -10.05   <2e-16 ***
## a   23.84555    1.53003   15.59   <2e-16 ***
## b  132.20661    6.39948   20.66   <2e-16 ***
## c  257.07744   23.79494   10.80   <2e-16 ***
## d    1.45077    0.08268   17.55   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5869 on 5204 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6770     3131.6                                
## 2   6769     3119.2  1 12.359  26.821 2.297e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 73749.96
## 2     2 73725.17
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  4.126e-01  1.878e-01   2.197   0.0281 *  
## phi 4.961e-02  8.995e-03   5.516  3.6e-08 ***
## a   1.625e+01  9.543e-01  17.027  < 2e-16 ***
## b   1.072e+02  4.832e+00  22.194  < 2e-16 ***
## c   2.120e+02  1.160e+01  18.278  < 2e-16 ***
## d   1.376e+00  5.654e-02  24.341  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6788 on 6769 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (5 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1   4432     1818.5                               
## 2   4431     1813.3  1 5.2046  12.718 0.000366 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 49380.46
## 2     2 49369.75
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.38596    0.22716   1.699 0.089375 .  
## phi   0.03892    0.01063   3.663 0.000252 ***
## a    18.80827    1.08906  17.270  < 2e-16 ***
## b   130.47290    6.45246  20.221  < 2e-16 ***
## c   137.56631    4.44177  30.971  < 2e-16 ***
## d     1.09670    0.03414  32.122  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6397 on 4431 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93137, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -19.315, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    710     277.98                            
## 2    709     276.92  1 1.0638  2.7236 0.09932 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7186.079
## 2     2 7185.338
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)
## ge  -3.341e-01  3.837e-01  -0.871    0.384
## phi  3.183e-02  1.948e-02   1.634    0.103
## a    5.701e+00  2.127e+01   0.268    0.789
## b    1.894e+02  5.143e+02   0.368    0.713
## c    5.000e+03  4.717e+04   0.106    0.916
## d    3.745e+00  4.918e+00   0.761    0.447
## 
## Residual standard error: 0.625 on 709 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95662, p-value = 1.105e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.8529, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    486     175.73                              
## 2    485     175.73  1 -1.6266e-10       0      1
##   model      AIC
## 1     1 4974.722
## 2     2 4976.722
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.3835     0.2579  -5.364 1.26e-07 ***
## a   18.5217     3.1507   5.879 7.70e-09 ***
## b  111.2733    12.4104   8.966  < 2e-16 ***
## c  220.2789    41.6622   5.287 1.88e-07 ***
## d    1.3201     0.1853   7.123 3.83e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6013 on 486 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90332, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.1527, p-value = 2.567e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 1
222 Midwest Broadleaf Forest 1
223 Central Interior Broadleaf Forest 1
231 Southeastern Mixed Forest 1
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest 1
251 Prairie Parkland (Temperate) 1
255 Prairie Parkland (Subtropical) 1
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest 1
313 Colorado Plateau Semi-Desert 1
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe 1
332 Great Plains Steppe 1
341 Intermountain Semi-Desert and Desert 1
342 Intermountain Semi-Desert 1
411 Everglades 1
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 1
M223 Ozark Broadleaf Forest Meadow NA
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 1
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 1
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow 1

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.2.5 ge.97.5 phi phi.2.5 phi.97.5 alpha alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 9943 3257 -0.2412335 -0.4497812 -0.0326858 0.0481211 0.0355012 0.0607409 NA NA NA 28.841474 26.469998 31.21295 131.42371 122.90701 139.94042 126.03678 115.50692 136.56663 1.1023765 1.0234745 1.1812786
212 Laurentian Mixed Forest east 30395 11945 0.1140061 -0.0127661 0.2407784 0.0000000 -0.0060365 0.0060365 NA NA NA 14.452839 13.671200 15.23448 92.71935 89.28687 96.15183 128.41078 120.45184 136.36973 1.4547033 1.3981993 1.5112073
221 Eastern Broadleaf Forest east 11294 4269 0.0170145 -0.1298727 0.1639017 NA NA NA NA NA NA 21.667151 18.721272 24.61303 174.62875 161.49729 187.76020 154.79638 133.38167 176.21110 1.5019436 1.3859194 1.6179677
222 Midwest Broadleaf Forest east 7913 3189 -0.1807390 -0.4002087 0.0387307 NA NA NA NA NA NA 16.597763 14.350454 18.84507 126.23170 117.37387 135.08952 116.00466 104.32712 127.68219 1.2269038 1.1336515 1.3201562
223 Central Interior Broadleaf Forest east 13446 4895 -0.0157796 -0.1443065 0.1127474 NA NA NA NA NA NA 21.632327 18.790866 24.47379 109.74919 103.93832 115.56005 116.08499 105.40672 126.76326 1.4434940 1.3403324 1.5466556
231 Southeastern Mixed Forest east 19961 7904 0.6880599 0.5391543 0.8369655 NA NA NA NA NA NA 13.360558 12.485458 14.23566 144.78186 136.37174 153.19199 142.55533 123.57446 161.53620 1.8732595 1.7807183 1.9658006
232 Outer Coastal Plain Mixed Forest east 20919 9046 0.2319657 0.0871922 0.3767392 0.0149078 0.0048896 0.0249261 NA NA NA 13.153721 12.107322 14.20012 165.02420 151.89072 178.15769 180.02788 146.42621 213.62954 1.9703357 1.8497826 2.0908888
234 Lower Mississippi Riverine Forest east 2190 937 -0.1275039 -0.5827497 0.3277420 0.0386612 0.0022919 0.0750306 NA NA NA 18.505068 10.787721 26.22242 249.58616 101.43803 397.73429 306.23891 -67.43450 679.91232 1.9773181 1.2749868 2.6796494
242 Pacific Lowland Mixed Forest pacific 246 172 -0.5603063 -1.5232964 0.4026838 NA NA NA NA NA NA 31.031987 -15.709302 77.77328 615.52160 310.16376 920.87944 352.76085 27.05174 678.46997 1.8421147 1.1323308 2.5518985
251 Prairie Parkland (Temperate) east 2787 1036 -0.3362390 -0.6409707 -0.0315074 NA NA NA NA NA NA 27.654337 22.912059 32.39661 103.81353 93.02980 114.59726 101.68632 88.65884 114.71380 1.1117727 0.9668465 1.2566990
255 Prairie Parkland (Subtropical) pacific 1288 659 -0.5128856 -1.0036203 -0.0221509 NA NA NA NA NA NA 14.244225 10.210621 18.27783 83.09090 71.37236 94.80944 69.99751 57.14508 82.84995 1.2098430 1.0119033 1.4077827
261 California Coastal Chaparral Forest and Shrub pacific 56 34 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 430 274 2.0492815 0.3941688 3.7043941 NA NA NA NA NA NA 0.000000 -110.170512 110.17051 1000.00000 -1170.07033 3170.07033 5000.00000 -31404.83509 41404.83509 3.4866144 -0.4503236 7.4235524
313 Colorado Plateau Semi-Desert interior west 508 312 -0.7864222 -1.4838778 -0.0889666 NA NA NA NA NA NA 25.473773 16.843973 34.10357 110.39796 87.25140 133.54453 131.74298 122.71833 140.76763 0.6679632 0.5549576 0.7809689
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 16 12 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 22 14 -1.1327584 -3.5895544 1.3240377 NA NA NA NA NA NA 0.000000 -32.609816 32.60982 256.16145 -966.20947 1478.53238 962.44169 -8993.78918 10918.67255 2.3078160 -2.9293683 7.5450004
322 American Semidesert and Desert interior west 8 5 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 753 473 -0.3459760 -1.3862004 0.6942484 NA NA NA NA NA NA 10.025225 4.966406 15.08404 54.45449 38.73241 70.17658 129.89998 75.05163 184.74833 1.4323237 0.9636546 1.9009929
332 Great Plains Steppe interior west 324 152 -0.2642535 -1.9235370 1.3950299 NA NA NA NA NA NA 24.216351 -6.142070 54.57477 321.73583 -3730.27597 4373.74763 1383.23171 -28960.55405 31727.01747 2.3260724 -6.1508064 10.8029511
341 Intermountain Semi-Desert and Desert interior west 147 93 1.2043907 -1.5075434 3.9163248 NA NA NA NA NA NA 29.351705 11.964479 46.73893 67.94252 31.18450 104.70055 141.86797 113.61703 170.11891 0.6582137 0.3819104 0.9345170
342 Intermountain Semi-Desert interior west 320 222 0.3773512 -2.0384323 2.7931346 NA NA NA NA NA NA 16.848265 6.279003 27.41753 48.34601 22.36602 74.32600 120.41512 96.44070 144.38954 0.8567007 0.5002262 1.2131751
411 Everglades east 170 86 -1.3900149 -2.5151636 -0.2648662 NA NA NA NA NA NA 11.069099 -38.867171 61.00537 934.14418 -12378.18402 14246.47237 5000.00000 -144580.06224 154580.06224 3.0309044 -7.5829445 13.6447533
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 10063 3398 0.0564998 -0.1226288 0.2356283 0.0296737 0.0190109 0.0403364 NA NA NA 15.085331 12.103749 18.06691 154.85207 141.25605 168.44808 186.83134 156.15760 217.50507 1.5844284 1.4492894 1.7195674
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 13165 4970 0.6699803 0.5263827 0.8135780 NA NA NA NA NA NA 27.603081 24.806265 30.39990 127.24722 122.14626 132.34818 107.28587 101.29932 113.27242 1.3513443 1.2784788 1.4242098
M223 Ozark Broadleaf Forest Meadow east 1248 392 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 1488 574 0.1658361 -0.3286921 0.6603644 0.0367390 0.0003998 0.0730783 NA NA NA 3.214899 -5.153137 11.58293 227.73280 -13.78808 469.25369 834.90949 -1423.37455 3093.19353 2.7372552 1.3633988 4.1111115
M242 Cascade Mixed Forest pacific 7940 4900 0.0089612 -0.3109837 0.3289061 NA NA NA NA NA NA 0.000000 -14.826575 14.82658 522.02082 440.82731 603.21433 863.30726 482.94235 1243.67218 2.5141501 2.1711867 2.8571134
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 4575 2761 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 54 38 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 913 563 -0.8261935 -1.3770856 -0.2753014 0.0291549 -0.0079966 0.0663063 NA NA NA 25.271882 14.788180 35.75558 111.54653 91.42690 131.66616 150.89398 127.91830 173.86967 0.8463537 0.6647606 1.0279467
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 5236 3514 -0.9834959 -1.1753756 -0.7916163 NA NA NA NA NA NA 23.845553 20.846057 26.84505 132.20661 119.66093 144.75228 257.07744 210.42936 303.72551 1.4507703 1.2886900 1.6128507
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 6780 4293 0.4125899 0.0444181 0.7807617 0.0496127 0.0319800 0.0672454 NA NA NA 16.248841 14.378155 18.11953 107.24863 97.77562 116.72164 212.02048 189.28104 234.75992 1.3761817 1.2653523 1.4870111
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 4440 2838 0.3859621 -0.0593855 0.8313096 0.0389236 0.0180926 0.0597546 NA NA NA 18.808270 16.673165 20.94337 130.47290 117.82286 143.12294 137.56631 128.85822 146.27439 1.0967019 1.0297679 1.1636359
M334 Black Hills Coniferous Forest interior west 716 364 -0.3341002 -1.0873426 0.4191422 0.0318262 -0.0064253 0.0700776 NA NA NA 5.701161 -36.067216 47.46954 189.39363 -820.25450 1199.04176 5000.00000 -87612.89848 97612.89848 3.7448342 -5.9114757 13.4011440
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 492 287 -1.3834885 -1.8902300 -0.8767470 NA NA NA NA NA NA 18.521694 12.331014 24.71237 111.27327 86.88860 135.65793 220.27885 138.41854 302.13916 1.3200946 0.9559446 1.6842445

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map #2

plot phi (effect of DeltaPDSI)

plot a coefficient

## Warning: Removed 7 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 7 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 11 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 7 rows containing missing values (geom_point).

Calculations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US  0.11415431
## 2       pacific  0.01943735
## 3          east  0.18894294
## 4 interior west -0.13979300

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.010287666
## 2       pacific  0.000000000
## 3          east  0.008045572
## 4 interior west  0.026665510

Calculations - weighted averages subsetted to 15 ecoprovinces

  • 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332,

ge

##          region weighted.ge
## 1     entire US 0.202434442
## 2       pacific 0.005731607
## 3          east 0.213926432
## 4 interior west 0.412589912

phi

##          region weighted.phi
## 1     entire US   0.01026246
## 2       pacific   0.00000000
## 3          east   0.00854629
## 4 interior west   0.04961268